Theory of free-electron lasers

A general analysis is presented of free-electron lasers in which a static periodic magnetic pump field is scattered from a relativistic electron beam. The steady-state formulation of the problem is fully relativistic and contains beam thermal effects. Growth rates associated with the radiation field, efficiencies, and saturated-field amplitudes are derived for various modes of operation. Effects of space charge on the scattering process are included and shown to play a dominant role in certain situations. Scaling laws for the growth rates and efficiencies at a fixed radiation frequency as a function of the magnetic-pump amplitude are obtained. The shear in beam axial velocity due to self-fields is discussed, and various methods of reducing it are suggested. Finally, a detailed illustration of a far-infrared ($\lambda =2\mathrm{}$ μm) two-stage free-electron laser using a 3-MeV electron beam and a 2-cm-wavelength magnetic pump field is presented.